ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 815 



L L are fixed, the object must be removed to a in order to get a distinct 

 image at the point P, and the greater the density of the fluid the longer the 

 distance from b. Hence bm, bn give the relative value of the refractive index 

 of the liquid under examination, and with a little calculation the absolute value 

 also. In his research Brewster kept the distance between the lenses invari- 

 able, and the thickness of the plano-convex lens identical, for all cases under 

 examination. The objects used were scratches on the surface of a piece of 

 glass. He adds an important detail which has been passed over by Smith. 

 Across the diaphragm at the anterior focus of the ocular he stretched a very 

 fine thread, which, as well as the mark in front of the objective, he tried to 

 keep distinctly in view, in order to prevent any error depending on the eye 

 of the observer. 



The fundamental principle of the two instruments is alike, although, in- 

 stead of a plano-convex lens of definite thickness, in the older apparatus the 

 thickness was variable. It is more convenient, however, for the artificial 

 lens to have constant dimensions as in Smith's apparatus, and not variable 

 ones as in Brewster's instrument, for when the distance which it is necessary 

 to remove the objective from the object in order to see it distinctly is known, 

 the calculation is readily made. 



A plate of glass is placed behind the objective, and the latter removed to 

 such a distance from the object (say a micrometer) that it is seen distinctly. 

 Let this distance be p. The cavity containing the liquid to be examined is 

 then placed behind the objective. In order that the eye behind the ocular 

 Q E may clearly distinguish the micrometer image at P, it becomes neces- 

 sary to remove the objective to a further point p'. Let P indicate the dis- 

 tance at which, in both cases, the image of the micrometer is formed behind 

 the objective ; / the focal length of the biconvex lens 6 ; /' that of 

 the added lens ; and F the focal length which results from the combina- 

 tion of the two lenses. 



From the law of conjugate foci 



By subtraction- 



or 



But 



— r ^ = -s and -, + ^ = v; . 

 pP / ^'^P F 



1_11_1_1_1_ 

 p p'^ F P~/ F' 



p p' f Y' 



F~f /'' 

 and on substituting this value in the previous equation we have 

 1_1^_1_11^_]^ 



Next let n be the index of refraction of the artificial lens, and r its radius 

 of curvature : then as 



1 _ n- 1 



we have 



1 _ 1 _ n - 1 



P p' ^ ' 



